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e differences in the average velocities (inc

e differences in the average velocities (inc

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The image displays plots of the relative numbers of N₂ (nitrogen) molecules that possess a given velocity at three different temperatures, measured in Kelvin. **Graph Explanation:** - **Title:** Molecular Velocity - **X-Axis:** Velocity (in meters per second) - **Y-Axis:** Number of N₂ (nitrogen) molecules The graph features three curves, each representing data at a distinct temperature: 1. **273 K (Kelvin):** This curve is the most peaked and narrowest, indicating a higher number of molecules at lower speeds. It highlights that at lower temperatures, most molecules move at relatively slower velocities. 2. **1273 K (Kelvin):** This curve is less steep and wider than the one for 273 K. It demonstrates a more distributed range of velocities, indicating that, as temperature increases, molecules achieve higher speeds. 3. **2273 K (Kelvin):** The curve is the flattest and widest, showing the widest range of molecular velocities. This represents the greatest spread of velocities and faster molecules at higher temperatures. This graph illustrates the relationship between temperature and molecular velocity, where higher temperatures lead to faster and more widely distributed molecular speeds.
Transcribed Image Text:The image displays plots of the relative numbers of N₂ (nitrogen) molecules that possess a given velocity at three different temperatures, measured in Kelvin. **Graph Explanation:** - **Title:** Molecular Velocity - **X-Axis:** Velocity (in meters per second) - **Y-Axis:** Number of N₂ (nitrogen) molecules The graph features three curves, each representing data at a distinct temperature: 1. **273 K (Kelvin):** This curve is the most peaked and narrowest, indicating a higher number of molecules at lower speeds. It highlights that at lower temperatures, most molecules move at relatively slower velocities. 2. **1273 K (Kelvin):** This curve is less steep and wider than the one for 273 K. It demonstrates a more distributed range of velocities, indicating that, as temperature increases, molecules achieve higher speeds. 3. **2273 K (Kelvin):** The curve is the flattest and widest, showing the widest range of molecular velocities. This represents the greatest spread of velocities and faster molecules at higher temperatures. This graph illustrates the relationship between temperature and molecular velocity, where higher temperatures lead to faster and more widely distributed molecular speeds.
Identify the differences in the average velocities (indicated by the peaks of the curves) for the three temperatures. As the temperature increases, the average velocity [Select]. For each temperature, the relative number of \( \text{N}_2 \) molecules [Select] until the peak of the curve and [Select] after the peak. Describe the intervals on which the velocity is increasing and decreasing for each of the three temperatures. (Enter your answers using interval notation.) - **At 273 K** - Increasing: [ ] - Decreasing: [ ] - **At 1273 K** - Increasing: [ ] - Decreasing: [ ] - **At 2273 K** - Increasing: [ ] - Decreasing: [ ]
Transcribed Image Text:Identify the differences in the average velocities (indicated by the peaks of the curves) for the three temperatures. As the temperature increases, the average velocity [Select]. For each temperature, the relative number of \( \text{N}_2 \) molecules [Select] until the peak of the curve and [Select] after the peak. Describe the intervals on which the velocity is increasing and decreasing for each of the three temperatures. (Enter your answers using interval notation.) - **At 273 K** - Increasing: [ ] - Decreasing: [ ] - **At 1273 K** - Increasing: [ ] - Decreasing: [ ] - **At 2273 K** - Increasing: [ ] - Decreasing: [ ]
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